Image Processing Method for Feature Retention and the System of the Same

ABSTRACT

The present invention discloses an image processing method for feature retention associated with averaging processes. The image processing method comprises: scaling and aligning a plurality of image data for acquiring feature information; determining a plurality of two-dimensional feature label points according to the feature information for generating at least one Bezier curve; utilizing the at least one Bezier curve to generate at least one Bezier tube and performing Bezier tube fitting for generating result of Bezier tube fitting; deforming the plurality of image data according to the Bezier tube or the result of Bezier tube fitting for generating a plurality of deformed image data; and averaging the plurality of deformed image data for generating feature-preserved average image data. The present invention also provides an image processing system, a computer readable storage medium, and a computer program product, for implementing the image processing method.

FIELD OF THE INVENTION

The present invention is generally related to an image processing methodand, more particularly, to an image processing method for featureretention associated with averaging a plurality of image data. Thefeature may be a surface feature of the images.

DESCRIPTION OF THE PRIOR ART

In the past decades, quite an endeavor has been devoted from academiaand industries to find out the structures and functions of the neuralnetwork in the human brain. However, this is a difficult task due to itsenormous number of neurons and complexities. To simplify this problem,in basic researches of life science, Drosophila (fruit flies), with thecapabilities of learning and memory, has been chosen as a model tofacilitate the understanding of structures and functions of the brainbecause the size and number of cells in a Drosophila brain are muchsmaller than in the human one. Moreover, it's relatively easy to getlarge number of samples out of fruit flies.

By using the confocal microscopy technology, individual Drosophilabrains may be scanned to get 2D brain image slices at designated depth.Moreover, by visualizing theses 2D brain image slices, a 3D brain modelimage can be constructed.

There are variations among the brain images acquired from the differentindividual Drosophila. Therefore, for generating a 3D Drosophila brainatlas, or Drosophila standard brain, it is necessary to carry out anaveraging procedure among those 3D brain images collected. However, inthe ordinary averaging procedure, the concave-shaped structures maydisappear during the process and result in a so-called close-up error.This may cause a serious deviation of the averaged model from the actualconcave-shaped structures in individual brain images. Specifically, theerrors are more critical in dealing with the surface structures, such asbrains, which have complicated sulci.

To overcome the shortcoming existed in the prior art, the presentinvention provides an image processing method for feature retentionassociated with averaging processes and the system of the same, which isdescribed in the following description.

SUMMARY OF THE INVENTION

For overcoming the shortcoming existed in the prior art, in one aspectof the present invention, an image processing method for featureretention associated with averaging a plurality of image data isprovided. The image processing method comprises: scaling and aligning aplurality of image data for acquiring feature information; determining aplurality of two-dimensional feature label points according to thefeature information for generating at least one Bezier curve; utilizingthe at least one Bezier curve to generate at least one Bezier tube andperforming Bezier tube fitting for generating result of Bezier tubefitting; deforming, by a processor, the plurality of image dataaccording to the Bezier tube or the result of Bezier tube fitting forgenerating a plurality of deformed image data; and averaging theplurality of deformed image data for generating feature-retainedaveraged image data.

In another aspect of the present invention, an image processing systemfor feature retention associated with averaging a plurality of imagedata is provided. The image processing system comprises: a controlmodule; a scaling and aligning module coupled to the control module, forscaling and aligning a plurality of image data for acquiring featureinformation; a Bezier curve fitting module coupled to the controlmodule, for determining a plurality of two-dimensional feature labelpoints according to the feature information for generating at least oneBezier curve; a Bezier tube fitting module coupled to the controlmodule, for utilizing the at least one Bezier curve to generate at leastone Bezier tube and performing Bezier tube fitting for generating resultof Bezier tube fitting; a deforming module coupled to the controlmodule, for deforming the plurality of image data according to theBezier tube or the result of Bezier tube fitting for generating aplurality of deformed image data; an averaging module coupled to thecontrol module, for averaging the plurality of deformed image data forgenerating feature-retained averaged image data; and a database modulecoupled to the control module, for storing data and/or informationgenerated by each of the modules.

Furthermore, in another aspect of the present invention, a computerreadable storage medium is provided. The storage medium stores a programof instructions executable by a computer to perform an image processingmethod for feature retention associated with averaging a plurality ofimage data.

In still another aspect of the present invention, a computer programproduct is provided. The computer program product comprises instructionsexecutable by a computer to perform an image processing method forfeature retention associated with averaging a plurality of image data.

By referring the following description and illustration of theembodiments of the present invention and the accompanying figures, theadvantages and the spirit of the present invention can be betterunderstood.

BRIEF DESCRIPTION OF THE DRAWINGS

The patent or application file contains at least one drawing executed incolor. Copies of this patent or patent application publication withcolor drawing(s) will be provided by the Office upon request and paymentof the necessary fee.

FIG. 1 illustrates an exemplary hardware for implementing theembodiments of the present invention;

FIG. 2 illustrates an image processing system according to theembodiments of the present invention;

FIGS. 3A-3D illustrate procedures of an image processing methodaccording to the embodiments of the present invention;

FIG. 4 illustrates an exemplary skeleton according to the embodiments ofthe present invention;

FIGS. 5A and 5B illustrate three-dimensional feature label points andcorresponding Bezier curves according to the embodiments of the presentinvention;

FIGS. 6A and 6B illustrate several Bezier curve segments according tothe embodiments of the present invention;

FIG. 7 illustrates a three-dimensional Bezier tube according to theembodiments of the present invention;

FIG. 8 illustrates the variation for capturing the feature according tothe embodiments of the present invention;

FIG. 9 illustrates the result of Bezier tube fitting according to theembodiments of the present invention;

FIG. 10 illustrates the result of the rigid transformation according tothe embodiments of the present invention;

FIG. 11 illustrates the relationship between the patches of the imagedata and the Bezier tube according to the embodiments of the presentinvention;

FIG. 12 illustrates the relationship between the vertex and the movementvector according to the embodiments of the present invention;

FIG. 13 illustrates the initial feature curve of nine brain modelaccording to the embodiments of the present invention;

FIG. 14 illustrates the feature curve after feature capturing procedureaccording to the embodiments of the present invention;

FIG. 15 illustrates the superimposition of the two image data before orafter the deformation procedure according to the embodiments of thepresent invention; and

FIGS. 16A-16D illustrate several superimpositions of the image databefore or after the deformation procedure according to the embodimentsof the present invention.

DESCRIPTION OF THE PREFERRED EMBODIMENT

An image processing method 30000 is provided in the embodiments of thepresent invention, as shown in FIGS. 3A-3D. For implementing the imageprocessing method 30000, an image processing system 20000 is provided inthe embodiments of the present invention, as shown in FIG. 2. Forimplementing the image processing system 20000, an exemplary hardware isprovided in the embodiments of the present invention, such as a computer10000, as shown in FIG. 1. The detailed description is provided asfollows.

FIG. 1 shows an exemplary hardware according to the embodiments of thepresent invention. In this embodiment, the hardware may be a computer10000 which comprises: a processing unit 11000; an image input interface12000 coupled to the processing unit 11000; a storage device interface13000 coupled to the processing unit 11000; a memory 14000 coupled tothe processing unit 11000; a configuration interface 15000 coupled tothe processing unit 11000; an image output interface 16000 coupled tothe processing unit 11000; an other interface or device 17000 coupled tothe processing unit 11000. The above-mentioned components may be coupledvia a bus 11100 or other forms. The storage device interface 13000 maycouple to a computer readable storage medium 13100 which stores acomputer program product. The instructions of the computer programproduct may be executed by a computer to perform the image processingsystem 20000 and thus the image processing method 30000. Moreover, thecomputer readable storage medium 13100 and the memory 14000 may storesoftware, such as, operating system, 13110, applications 13120,programming language and corresponding compiler 13130 and/or otherprogram 13140. The processing unit 11000 may be implemented by variousprocessors and, more particularly, by a programmable processor for somespecific purpose.

The image data may be received by the image input interface 12000, froman image providing device 12200 via an image input channel 12100. Inpreferred embodiments, 1 to N^(th) (N is a natural number being largeror equal to 2) image data of the surface model of Drosophila brains arereceived and then stored in the computer readable storage medium 13100and/or memory 14000, for facilitating the processing by the imageprocessing system 20000. Moreover, the parameters required within theimage processing system 20000 may be configured by a user via theconfiguration interface 15000 or by a predetermined program. The imagedata within different stage of the image processing method 30000 may bedisplayed on a display 16200 by an image output interface 16000 via animage output channel 16100. The image providing device 12200 maycomprise a confocal microscopy device, for scanning the individualDrosophila brains and acquiring their brain surface model data. Therelated imaging technique may refer to U.S. patent application Ser. No.11/169,890 “Bio-Expression System and the Method of the Same”. Further,other interface or device 17000 may widely refer to other neededinterfaces and/or devices which are not illustrated. In the preferredembodiments, the other interface or device 17000 may comprise networkports and wired or wireless network devices, for coupling to at leastone remote computer 17200 via wired or wireless network channel 17100.Hence, the qualified remote computer 17200 may command the computer10000 (more specifically, the database module 27000) to send the imagedata to the remote computer 17200 for further utilization. The remotecomputer 17200, used herein, is widely referring to any device beingable to receive and use the above-mentioned image data.

FIG. 2 shows the image processing system 20000 according to theembodiments of the present invention. In FIG. 2, the image processingsystem 20000 comprises: a control module 21000; a scaling and aligningmodule 22000 coupled to the control module 21000, for scaling andaligning the 1 to N^(th) image data of the surface model of theDrosophila brain received by the image input interface 12000, forreducing the main variation between the image data and thus facilitatingcapturing feature information; a Bezier curve fitting module 23000coupled to the control module 21000, for performing Bezier curve fittingprocedure; a Bezier tube fitting module 24000 coupled to the controlmodule 21000, for performing Bezier tube fitting procedure according tothe Bezier curve (more specific, a result of Bezier tube fitting may bepositioned to the N sets of data, or the Bezier curve configured by theuser may be positioned to the N sets of data for performing Bezier tubefitting, wherein the Bezier tube fitting module 24000 may receive theBezier curve, form the Bezier tube, and perform the fitting); adeforming module 25000 coupled to the control module 21000, fordeforming the plurality of image data (surface model) according to theBezier tube or the result of Bezier tube fitting for generating aplurality of deformed image data; an average module 26000 coupled to thecontrol module 21000, for averaging the plurality of deformed image datafor generating feature-retained averaged image data 26100; and adatabase module 27000 coupled to the control module 21000, for storing(temporarily or permanently) the data and/or information generated byeach of the above-mentioned modules. The detailed processing proceduresare described in the following paragraph.

FIGS. 3A-3D show the procedures of the image processing method 30000according to the embodiments of the present invention. In FIG. 3A, theimage processing method 30000 comprises: in step 31000, scaling andaligning a plurality of image data (image data 1 to N^(th)) foracquiring feature information; in step 32000, determining a plurality of2D feature label points according to the feature information forgenerating at least one Bezier curve; in step 33000, utilizing the atleast one Bezier curve to generate at least one Bezier tube andperforming Bezier tube fitting for generating result of Bezier tubefitting; in step 34000, deforming the plurality of image data accordingto the Bezier tube or the result of Bezier tube fitting for generating aplurality of deformed image data; and in step 35000, averaging theplurality of deformed image data for generating feature-retainedaveraged image data. In preferred embodiments, the step 34000 isexecuted by a processor. For brevity, the image processing method 30000may be viewed as follows: the step 31000 to 33000 may substantially beviewed as selecting and establishing a reference of feature informationfrom a plurality of image data; the step 34000 may be substantiallyviewed as computing the relationships between each of the image data andtheir Bezier tubes, deforming their Bezier tube, so as to deform (changethe shape of) the model in the image data, and the step 35000 mayaverage all the deformed model of the image data for acquiringfeature-retained averaged data.

FIG. 3B illustrates the more detailed procedures of the image processingmethod 30000. In FIG. 3B, the image processing method 30000 comprises:in step 31100, executing the application 13120 stored in the computerreadable storage medium 13100 by the processing unit 11000, forreceiving and storing the 1 to N^(th) image data from the image inputinterface 12000 to the database module 27000 by the control of thecontrol module 21000; in step 31200, capturing, scaling, and aligningthe 1 to N^(th) image data from the database module 27000 by utilizingthe scaling and aligning module 22000, for reducing (or eliminating) themain (substantial) variations between the image data, whereby featureinformation may be determined; the scaled and aligned image data may bestored in the database module 27000; the image data and the featureinformation may be displayed on a display 16200 by utilizing the imageoutput interface 16000 via the image output channel 16100; the featureinformation may be, such as, concave-shaped structure, which representsthe common concave-shaped structure on almost all Drosophila brain imagedata; in step 32100, the user may input instruction 23100 to select theimage data, by utilizing the configuration interface 15000, which issent to the Bezier curve fitting module 23000, for selecting at leastone of the 1 to N^(th) image data as a reference image data (otherwise,the image data may be select by a computer program); in step 32200, theuser (utilizing the configuration interface 15000) or the computerprogram may input instructions 23200 for configuring a plurality of 2Dfeature label points to the reference image data according to thefeature information, for generating a plurality of 2D feature labelpoints; in step 32300, generating a plurality of 3D feature label pointsaccording to the plurality of 2D feature label points by utilizing theBezier curve fitting module 23000; in step 32400, generating at leastone Bezier curve according to the plurality of 3D feature label pointsby implementing least square procedure; in step 33100, transferring(ballooning) the at least one Bezier curve to at least one Bezier tube,by utilizing the Bezier tube fitting module 24000; in step 33200,fitting, by utilizing the Bezier tube fitting module 24000, thereference image data according to the at least one Bezier tube, forgenerating result of Bezier tube fitting of the reference image data;fitting the 1 to N^(th) image data according to the Bezier tube or theresult of the Bezier tube fitting of the reference image data, forgenerating a plurality of Bezier tube control points for each imagedata; in step 34100, averaging, by utilizing the deforming module 25000,the plurality of Bezier tube control points of the 1 to N^(th) imagedata, for generating a plurality of averaged Bezier tube control points;in step 34200, computing, by utilizing the deforming module 25000, thetransformation of each of the plurality of Bezier tube control points ofthe 1 to N^(th) image data relative to the plurality of averaged Beziertube control points, for generating the transformation information ofeach of the 1 to N^(th) image data; in step 34300, deforming, byutilizing the deforming module 25000, the 1 to N^(th) image dataaccording to the transformation information for each of the 1 to N^(th)image data and correspondence map of each of the 1 to N^(th) image data,wherein the correspondence map of each of the 1 to N^(th) image data isgenerated by fitting the Bezier tube control points of the k^(th) imagedata and the k^(th) image data being scaled and aligned; in step 35100,averaging, by utilizing the averaging module 26000, the 1 to N^(th)deformed image data, for generating feature-retained averaged image data26100; and in step 35200, transmitting, by utilizing the image outputinterface 16000, the feature-retained averaged image data to the display16200 or transmitting, via wired or wireless network channel 17100, thefeature-retained averaged image data to a remote computer 17200.

In some embodiments of the present invention, in step 31200, the rigidtransformation procedure may be applied. The rigid transformationprocedure may be defined as:

x′=R(x−C)+C+T

Where the position of an arbitrary point before rigid transformation isx=[x, y, z]^(T), and x′ is the new position. C=[C_(x), C_(y), C_(z)]^(T)is the center of rotation. T=[T_(x), T_(y), T_(z)]^(T) is thetranslation matrix. R is the rotation matrix. Moreover, a good criterionto determine how two image data (surface) are alike (whether they havebeen appropriately scaled and aligned or not) is to measure the distancebetween them. In one embodiment, after several iterations, the result ofrigid transformation is shown in FIG. 10.

In the preferred embodiments, a graphical user interface (GUI) programis designed to let users label specific features of a 3D model (morespecifically, surface model) with a 2D operation system. And the labelselection procedure may also find out the depth information of eachlabel feature point. In FIG. 3C, the step 32300 comprises: in step32310, by utilizing the Bezier curve fitting module 23000, a vector(trajectory vector) being vertical to the 2D observation plane isgenerated according to each of 2D feature label points; in step 32320,sending, by utilizing the Bezier curve fitting module 23000, the vectorsto penetrate through the surface model of the k^(th) image data; in step32330, finding, by utilizing the Bezier curve fitting module 23000, aplurality of patch being penetrated by the vectors of each of 2D featurelabel points of the k^(th) image data, wherein the k^(th) image data issubstantially referring to the selected reference image data (it is alsosuitable for other image data); in step 32340, computing, by utilizingthe Bezier curve fitting module 23000, the middle values (positions) ofthe plurality of the patches (or patch groups); and in step 32350,assigning the middle values (positions) as the positions of the 3Dfeature label points. It should be noted that since most of the surfacemodels are closed, the vector may pass through the surface model atleast twice (penetrate into the surface model first and then penetrateout of it). By calculating the middle point between these two penetratedpatches and assigning the position of the middle point as the positionof the 3D feature label point, the 3D feature label points are ensuredto be inside the 3D surface models in most of the conditions.

In preferred embodiment, as shown in FIG. 3D, the step 32400 comprises:in step 32410, dividing, by utilizing the Bezier curve fitting module23000, the plurality of 3D feature label points into groups (utilizingseveral 3D feature label points as a group to find out a curve), forgenerating a plurality of 3D feature label point groups; in step 32420,assigning, by utilizing the Bezier curve fitting module 23000, the firstand last label points of each of the plurality of 3D feature label pointgroups as each of the first and last Bezier curve control points; and instep 32430, finding, by utilizing Bezier curve fitting module 23000, themiddle Bezier curve control points between the first and last Beziercurve control points by applying the least square procedure. Inpreferred embodiments, the step 32430 comprises: in step 32431,generating, by utilizing the Bezier curve fitting module 23000, a leastsquare cost function; and in step 32432, finding, by utilizing theBezier curve fitting module 23000, the middle Bezier curve controlpoints by applying the first order derivative procedure to the leastsquare cost function. The m^(th) order Bezier curve may be expressed as:

${{C\left( t_{i}\; \right)} = {\sum\limits_{k = 0}^{m}{\begin{pmatrix}m \\k\end{pmatrix}\left( {1 - t_{i}}\; \right)^{m - k}t_{i}^{k}\; P_{k}}}},{0 \leq t_{i} \leq 1}$

Where C(t_(i)) is an interpolated point at parameter value t_(i) (anypoint of the m-order Bezier curve, or refer as “curve point”), m isdegree of Bezier curve, and P_(k) is the k^(th) control point. Togenerate n point (n is count of interpolating points) between the firstand last Bezier curve control points inclusive, the parameter t_(i) isuniformly divided into n−1 intervals between 0 and 1 inclusive. Therepresentation of a cubic Bezier curve is as follows:

C(t _(i))=(1−t _(i))³ P ₀+3t _(i)(1−t _(i))² P ₁+3t _(i) ²(1−t _(i))P ₂+t _(i) ³ P ₃

The Bezier curve will pass through its first and last control points.And the middle Bezier curve control points, i.e., P₁ and P₂, should bedetermined Instead of using time-consuming iterative optimizationprocess to locate P₁ and P₂, a least square procedure based on thefirst-order partial derivative procedure is applied. The least squareprocedure gives the better locations of the middle control points thatminimize the square distance between original input feature label pointsand the fitted points and is well suited for approximating data. Supposethat there are n 3D feature label points to be fitted, p_(i) andC(t_(i)) are values of the original 3D feature label points and theapproximated Bezier curve points respectively. The least square costfunction may be expressed as follows:

${F = {\sum\limits_{i = 1}^{n}\left\lbrack {{C\left( t_{i} \right)} - p_{i}} \right\rbrack^{2}}},{or}$$F = {\sum\limits_{i = 1}^{n}\left\lbrack {{\left( {1 - t_{i}} \right)^{3}P_{0}} + {3{t_{i}\left( {1 - t_{i}} \right)}^{2}P_{1}} + {3{t_{i}^{2}\left( {1 - t_{i}} \right)}P_{2}} + {t_{i}^{3}P_{3}} - p_{i}} \right\rbrack^{2}}$

By applying the first-order partial derivatives to the cost function,the middle Bezier curve control points may be obtained. The P₁ and P₂can be determined by:

${\frac{\partial F}{\partial P_{1\;}} = 0},{{{and}\mspace{14mu} \frac{\partial F}{\partial P_{2}}} = 0}$

After determining the Bezier curve control points, the cubic Beziercurves may fit large number of original 3D feature label points shown inFIGS. 5A and 5B. FIGS. 5A and 5B illustrate the 3D feature label pointsand corresponding Bezier curves according to the embodiments of thepresent invention. In preferred embodiments, to get more accuratefitting result, the original digitized curve (labeled points) may be cutinto multiple curve segments, and then the least square fittingprocedure may be applied to each of the curve segments. The fittingresults are shown in FIGS. 6A and 6B. FIGS. 6A and 6B illustrate severalBezier curve segments according to the embodiments of the presentinvention. It is shown that by applying several Bezier curve segments,the Bezier curve is more accurately fitted to the corresponding 3Dfeature label points.

In the preferred embodiments, in the step 33100, each circle withdiameter R centered at C(t_(i)) on each curve is inserted, and thecircle is orthogonal to the tangent of the corresponding curve point.FIG. 7 shows the result after ballooning procedure in step 33100. Thecurve after ballooning procedure is referred as “cubic Bezier tube”. Thecenter line of the tube is a cubic Bezier curve interpolated by its fourBezier curve control points. The notation, CyPt(i,j), refers as thej^(th) cylinder balloon points on the i^(th) circle. In the preferredembodiments, at least one Bezier tube is fitted to the reference imagedata, for generating result of the Bezier tube fitting. In preferredembodiments, the step 33200 comprises moving and relocating the at leastone Bezier curve in space, for more accurately defined the feature ofthe image data, as shown in FIG. 8. FIG. 8 illustrates the variation forcapturing the feature according to the embodiments of the presentinvention, such as the result from the step 33200. In the step 33200, a3D distance map is applied. The 3D distance map is a volumetric datasetthat represents the closest distance information. Given a geometricobject (surface model image data) in 3D space, the 3D distance mapdefines the shortest distance d(x) from a point xεR³ to the object. Orequivalently:

${{DistMap}(x)} = {\min\limits_{\forall k}\left\{ {\left. {d(x)} \middle| {d(x)} \right. = {{x - p_{k}}}} \right\}}$

The above procedure is distance-based. Therefore, it is necessary tofind the relationship of the average distance (ie., the system cost)between the multi-segment cubic Bezier tube and the surface model of theimage data, for minimizing the system cost iteratively. The averagedistance for the k^(th) tube segment, E_(k), is defined as follows:

$E_{k} = {\frac{1}{NM}{\sum\limits_{i = 1}^{N}{\sum\limits_{j = 1}^{M}{d^{2}\left( {{CyPt}_{k}\; \left( {i,j} \right)} \right)}}}}$

Where d(x) is the recorded value of DistMap(x).

By using gradient descent procedure, the cost function E_(k) may beminimized After several iterations, the position of the Bezier tube maybe optimized, as shown in FIG. 9, and the plurality of optimized Beziertube control points may be obtained. In other words, the 33200 may betreated as fitting the 1 to N^(th) image data according to the Beziertube or the result of the Bezier tube fitting of the reference imagedata. The Bezier tube or the result of the Bezier tube fitting of thereference image data may be positioned to the 1 to N^(th) image data tobe assigned as the initial position of their Bezier tube. Then, theresult of Bezier tube fitting of the 1 to N^(th) image data is obtainedby applying the Bezier tube fitting procedure.

In the preferred embodiments, in step 34100, the averaging procedure mayonly be applied to the plurality of the Bezier tube control points, butnot to all the discrete curve points. The averaged Bezier tube controlpoints may be expressed as follows:

$P_{avg} = {\frac{\sum\limits_{j = 1}^{m}\begin{bmatrix}P_{0\; j} \\P_{1j} \\P_{2j} \\P_{3j}\end{bmatrix}}{m} = \frac{\sum\limits_{j = 1}^{m}\begin{bmatrix}x_{0j} & {y_{0j}\;} & z_{0j} \\x_{1j} & y_{1j} & z_{1j} \\x_{2j} & y_{2j} & z_{2j} \\x_{3j} & y_{3j} & z_{3j}\end{bmatrix}}{m}}$

Where m refers to the number of the cubic Bezier curve. Once theaveraged Bezier tube control points are determined, the center line ofthe averaged Bezier tube may be constructed by applying the followingequation:

$\begin{matrix}{{B_{avg}(t)} = {\sum\limits_{i = 0}^{3}{\begin{pmatrix}3 \\i\end{pmatrix}\left( {1 - t} \right)^{3 - i}t^{i}P_{iavg}}}} \\{= {{\left( {1 - t} \right)^{3}P_{0{avg}}} + {\begin{pmatrix}3 \\1\end{pmatrix}\left( {1 - t} \right)^{2}t^{1}P_{1{avg}}} + {\begin{pmatrix}3 \\2\end{pmatrix}\left( {1 - t} \right)^{1}t^{2}P_{2{avg}}} +}} \\{{t^{3}P_{3{avg}}}}\end{matrix}$

Where tε[0,1].

In the preferred embodiments, in the step 34200, the translocation froman arbitrary point on the individual Bezier tube B_(ind)(t_(m)) to thesame index point on the averaged Bezier tube B_(avg)(t_(m)) is computed.The difference of these two points can be written as the weighting sumof the differences of the Bezier tube control points because these twopoints can be described by linear equations:

${{B_{{avg}\;}\left( t_{m} \right)} - {B_{ind}\left( t_{m} \right)}} = {\sum\limits_{i = 0}^{3}{\begin{pmatrix}3 \\i\end{pmatrix}{t_{m}^{i}\left( {1 - t_{m}} \right)}^{n - i}\left( {P_{i,{avg}} - P_{i,{ind}}} \right)}}$

Using the equation above, the matrix of the translocation thatrepresents the movement of curve points may be generated.

In the preferred embodiments, in the step 34300, the averaged Beziertube (averaged Bezier tube control points) is utilized as skeleton orskeleton-like, for controlling the deformation of the 1 to N^(th) imagedata. FIG. 4 shows the skeleton or skeleton-like mentioned herein. Inthe following procedures, the skeleton is utilized to adjust the imagedata, for ensuring they have similar concave-shaped structure. In orderto figure out the belonging skeleton point for each vertex on thesurface model, the 3D Euclidian distance between each vertex and pointon Bezier curves is measured. Since the Bezier curve plays a“skeleton-like” role, the correspondence between each vertex and Beziercurve will be higher if the measurement of Euclidian distance is less(and vice versa). Therefore, it just needs to take the nearest curvepoint as the correspondence point for any vertex point as shown in FIG.11. FIG. 11 shows the correspondence of the vertex of patch n of theimage data and the Bezier tube, for finding the weight of deformation.The deformation weighting tends to have the following characteristics:

-   1. The weighting may be less as the distance between a vertex and    its correspondence point on the curve is longer;-   2. If distance <R, the vertex shall follow the whole corresponding    movement vector (100%), that is the weighting may be 1;-   3. If distance >R+λ, the vertex shall ignore corresponding movement    vector (0%), that is the weighting will be approximately 0.

R is the radius of Bezier tube, and λ is the distance of the decay. Tobe natural, deformation weighting requires a smooth nonlinear function,like the sigmoid function, which has an “s” shape and climbs upsmoothly:

${f(t)} = \frac{1}{1 + ^{- t}}$

The scaled and transferred sigmoid function with α and β can beconsidered as a smooth weighting function. Using the sigmoid function,the new vertex position may be calculated as follows:

$\begin{matrix}{{{NewVertex}({Index})} = {{{Vertex}({Index})} + {{Movement} \times \frac{1}{1 + ^{\alpha {({{dist} - \beta})}}}}}} \\{= {{{Vertex}({Index})} + {moving}}}\end{matrix}$

The movement is the correspondence point movement of any vertex. Themultiple deformation field is the combination of the whole processmentioned above, with the vertex point on a shape model being controlledby multiple curves, as shown in FIG. 12, wherein the distance betweenthe vertex 41000 and the correspondence points on each Bezier tube are43100, 43200, and 43300, and the movement vectors are 44100, 44200, and44300. Moreover, the deformation procedure may utilize the equation asfollows:

${NewVertexData} = {{vertexData} + \frac{\sum\limits_{i = 1}^{n}{{Movement}_{i} \times \frac{1}{1 + ^{\alpha {({{Dist}_{i} - \beta})}}} \times \frac{1}{1 + ^{\gamma {({{Dist}_{i} - \eta})}}}}}{\sum\limits_{i = 1}^{n}\frac{1}{1 + ^{\gamma {({{Dist}_{i} - \eta})}}}}}$

Where α, β, γ, and η are the sigmoid function scaling and transferredvariables. Using the equation above, all vertices vertexData may bedeformed to have averaged appearance (new vertices NewVertexData) usingthose movements Movement generated by Bezier curves.

In the preferred embodiments, in the step 35100, the averaging proceduremay comprise signed distance map (SDM) averaging procedure whichcomprises:

-   1. Transform the shape model into the volume model and cut into    slices;-   2. Create SDM of slices;-   3. Cumulatively sum up the SDM slice of each shape model and find    the zero contour as averaged contour;-   4. Stack up the zero contour and obtain the averaged 3D contour;-   5. Transform 3D contour to shape model (wireframe).

In the preferred embodiments, the initial feature curve of nine brainmodel are shown as FIG. 13 (Refer to step 33200, projecting the Beziertube of the reference image data to those 1 to N^(th) image data, as theinitial position of the Bezier tubes).

The result generated after the process of step 33200 is shown in FIG.14. In FIG. 14, it can be observed that the feature of each image datamay be well captured after the Bezier tube fitting procedure. Moreover,FIG. 15 shows the superimposition of the two image data before or afterthe deformation procedure according to the embodiments of the presentinvention. It can be observed that the extent of the superimposition ofthe two image data is improved with the deformation procedure, forfacilitating retaining important feature of the image data with (after)averaging procedure.

Furthermore, FIG. 16A shows the superimposition of three image datawithout deformation. FIG. 16B shows the superimposition of three imagedata with deformation. FIG. 16C shows the averaged image data withoutdeformation. FIG. 16D shows the averaged image data with deformation.Open the circle marks signed in the FIGS. 16A to 16D, it can be observedthat the features, such as the concave-shaped structures, are reasonablywell retained with the process of the method according to theembodiments of the present invention. In contrast, most of the featuresare lost without the process of the method. The lost of the featureinformation makes the such formed standard brain model invalid.

The above descriptions are the preferred embodiments of the presentinvention. They are intended to explain the present invention but notlimit the range of the present invention. The range of the presentinvention should base upon the claims and their equivalences. Thevariation and modification made by others without departing the rangeand the spirit of the present invention may be viewed as the equivalenceof the present invention.

1. An image processing method for feature retention associated withaveraging a plurality of image data, said image processing methodcomprising: scaling and aligning a plurality of image data for acquiringfeature information; determining a plurality of two-dimensional featurelabel points according to said feature information for generating atleast one Bezier curve; utilizing said at least one Bezier curve togenerate at least one Bezier tube and performing Bezier tube fitting forgenerating result of Bezier tube fitting; deforming, by a processor,said plurality of image data according to said Bezier tube or saidresult of Bezier tube fitting for generating a plurality of deformedimage data; and averaging said plurality of deformed image data forgenerating feature-retained averaged image data.
 2. The image processingmethod according to claim 1, further comprising utilizing an imageoutput interface to transmit said feature-retained averaged image datato a display or utilizing a wired or wireless network to transmit saidfeature-retained averaged image data to a remote computer.
 3. The imageprocessing method according to claim 1, wherein step of said determininga plurality of two-dimensional feature label points according to saidfeature information for generating at least one Bezier curve comprises:utilizing said plurality of two-dimensional feature label points togenerate a plurality of three-dimensional feature label points; andutilizing least square procedure to generate said at least one Beziercurve according to said plurality of three-dimensional feature labelpoints.
 4. The image processing method according to claim 3, whereinstep of said utilizing said plurality of two-dimensional feature labelpoints to generate a plurality of three-dimensional feature label pointscomprises: generating a plurality of vectors being vertical totwo-dimensional observation plane according to said plurality oftwo-dimensional feature label points; sending said plurality of vectorsto penetrate through said image data; finding a plurality of patchgroups being penetrated by said plurality of vectors; finding middlepositions of said plurality of patch groups to obtain a plurality ofmiddle points; and setting said plurality of middle points as saidplurality of three-dimensional feature label points.
 5. The imageprocessing method according to claim 3, wherein step of said utilizingleast square procedure to generate said at least one Bezier curveaccording to said plurality of three-dimensional feature label pointscomprises: dividing said plurality of three-dimensional feature labelpoints into a plurality of three-dimensional feature label point groups;generating a plurality of Bezier curve segments according to saidplurality of three-dimensional feature label point groups; andgenerating said at least one Bezier curve according to said plurality ofBezier curve segments.
 6. The image processing method according to claim5, wherein step of said generating a plurality of Bezier curve segmentsaccording to said plurality of three-dimensional feature label pointgroups comprises: utilizing a least square procedure to generate a leastsquare cost function according to said plurality of three-dimensionalfeature label point groups; utilizing a first-order partial derivativeprocedure to said least square cost function to find middle Bezier curvecontrol points of said plurality of three-dimensional feature labelpoints; and generating said plurality of Bezier curve segments accordingto said plurality of three-dimensional feature label point groups andsaid middle Bezier curve control points.
 7. The image processing methodaccording to claim 1, wherein step of said deforming said plurality ofimage data according to said Bezier tube or said result of Bezier tubefitting for generating a plurality of deformed image data comprisesfinding deformation weights.
 8. The image processing method according toclaim 1, wherein said deforming said plurality of image data accordingto said Bezier tube or said result of Bezier tube fitting for generatinga plurality of deformed image data comprises a non-linear functionprocessing procedure.
 9. The image processing method according to claim1, wherein step of said averaging said plurality of deformed image datafor generating a feature-retained averaged image data comprises a signeddistance map averaging procedure.
 10. The image processing methodaccording to claim 1, wherein said plurality of image data arethree-dimensional brain model image data.
 11. The image processingmethod according to claim 1, wherein said feature information isconcave-shaped structure information of brain model image.
 12. An imageprocessing system for feature retention associated with averaging aplurality of image data, said image processing system comprising acontrol module; a scaling and aligning module coupled to said controlmodule, for scaling and aligning a plurality of image data for acquiringfeature information; a Bezier curve fitting module coupled to saidcontrol module, for determining a plurality of two-dimensional featurelabel points according to said feature information for generating atleast one Bezier curve; a Bezier tube fitting module coupled to saidcontrol module, for utilizing said at least one Bezier curve to generateat least one Bezier tube and performing Bezier tube fitting forgenerating result of Bezier tube fitting; a deforming module coupled tosaid control module, for deforming said plurality of image dataaccording to said Bezier tube or said result of Bezier tube fitting forgenerating a plurality of deformed image data; an averaging modulecoupled to said control module, for averaging said plurality of deformedimage data for generating feature-retained averaged image data; and adatabase module coupled to said control module, for storing data and/orinformation generated by each of said modules.
 13. The image processingsystem according to claim 12, wherein said plurality of image data arethree-dimensional Drosophila brain model image data.
 14. The imageprocessing system according to claim 12, wherein said featureinformation is concave-shaped structure information of brain modelimage.
 15. A computer readable storage medium, said storage mediumstoring a program of instructions executable by a computer to perform animage processing method for feature retention associated with averaginga plurality of image data, said storage medium comprising instructionsto: scale and align a plurality of image data for acquiring featureinformation; determine a plurality of two-dimensional feature labelpoints according to said feature information for generating at least oneBezier curve; utilize said at least one Bezier curve to generate atleast one Bezier tube and perform Bezier tube fitting for generatingresult of Bezier tube fitting; deform said plurality of image dataaccording to said Bezier tube or said result of Bezier tube fitting forgenerating a plurality of deformed image data; and average saidplurality of deformed image data for generating feature-retainedaveraged image data.
 16. A computer program product comprisinginstructions executable by a computer to perform an image processingmethod for feature retention associated with averaging a plurality ofimage data, said computer program product comprising: instructions toscale and align a plurality of image data for acquiring featureinformation; instructions to determine a plurality of two-dimensionalfeature label points according to said feature information forgenerating at least one Bezier curve; instructions to utilize said atleast one Bezier curve to generate at least one Bezier tube and performBezier tube fitting for generating result of Bezier tube fitting;instructions to deform said plurality of image data according to saidBezier tube or said result of Bezier tube fitting for generating aplurality of deformed image data; and instructions to average saidplurality of deformed image data for generating feature-retainedaveraged image data.